{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NUK73NOMJUGAIPOJHYSL5VZXOT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b1642fb8cb67cbc6e0dce112b5c221c64ed645706e33048a5d4dd5da176b9279","cross_cats_sorted":["math.NA","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2016-02-23T15:42:43Z","title_canon_sha256":"5617afdbfbfa4aaaadc427f3ffe4137a86d7a7d7ae74f2c1852a7af13f6810ca"},"schema_version":"1.0","source":{"id":"1602.07205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07205","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07205v2","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07205","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"NUK73NOMJUGA","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NUK73NOMJUGAIPOJ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NUK73NOM","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:d1765901c9cabc7be2823d5a5a5ff4b4a059ab413e22b0cdb13112d88e2be28d","target":"graph","created_at":"2026-05-18T01:12:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A fractional time derivative is introduced into the Burger's equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equations. Then a quadrature formula yields a system of local partial differential equations, well-suited to numerical integration. The determination of the quadrature coefficients is crucial to ensure both ","authors_text":"Bruno Lombard, Denis Matignon","cross_cats":["math.NA","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2016-02-23T15:42:43Z","title":"Diffusive approximation of a time-fractional Burger's equation in nonlinear acoustics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07205","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:20d09642a2c147213148becddd4b2420e6bbd5a9e05fdcfbd67ff479c5be9f14","target":"record","created_at":"2026-05-18T01:12:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b1642fb8cb67cbc6e0dce112b5c221c64ed645706e33048a5d4dd5da176b9279","cross_cats_sorted":["math.NA","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2016-02-23T15:42:43Z","title_canon_sha256":"5617afdbfbfa4aaaadc427f3ffe4137a86d7a7d7ae74f2c1852a7af13f6810ca"},"schema_version":"1.0","source":{"id":"1602.07205","kind":"arxiv","version":2}},"canonical_sha256":"6d15fdb5cc4d0c043dc93e24bed73774d77e6d7f6dbed7e0d6b7629dcd71d178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d15fdb5cc4d0c043dc93e24bed73774d77e6d7f6dbed7e0d6b7629dcd71d178","first_computed_at":"2026-05-18T01:12:34.447252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:34.447252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VM3lLjTVcmIHDCZ5H6uhSaGv2bH8d2RYk0QTxFBd7yrHJMHKNKDaSx0OEYmImc2hlwslsFHkcVCnjfeguimdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:34.447675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d09642a2c147213148becddd4b2420e6bbd5a9e05fdcfbd67ff479c5be9f14","sha256:d1765901c9cabc7be2823d5a5a5ff4b4a059ab413e22b0cdb13112d88e2be28d"],"state_sha256":"9997bf4fe3e983f2bfcf0fb767013ed49a561722281d9fbda34b352cc3e55405"}